Properties of Solids and Liquids
= Solids = Elasticity The property of a body , by the virtue of which material bodies regain their original dimensions (size , shape or both ) after removal of deforming forces is called elasticity . Plasticity Plasticity is the property of a body to undergo permanent deformation even after the removal of deforming forces . Rigidity Deformation α Deforming Force Strain α Stress Stress / Strain = Constant Stress And Strain 1) Longitudinal Stress & Strain (along length) Longitudinal Stress = Applied Force / Cross Section Area Longitudinal Strain = ( l - l0 ) / l0 = ∆L / L 2) Volume Stress & Strain (with Volume) Volume Stress = Applied Force / Volume Volume Strain = ∆V / V 3) Shearing Stress & Strain (with shape) Shearing Stress = Tangential Applied Force / Area Shearing Strain = θ Elasticity Modulus (Hooke's Law) (Young's Modulus and Hooke's Law for JEE) Deformation α Deforming Force Strain α Stress Stress / Strain = M ; where M is a constant , called as Modulus of Elasticity . Young's Modulus (for longitudinal strain and stress) Y = Longitudinal Stress / Longitudinal Strain Bulk Modulus (for Volume Strain and Strain) K = Volume Stress / Volume Strain Compressibility = 1 / Bulk Modulus Modulus of Rigidity (for Shearing Strain and Stress) η = Shearing Stress / Shearing Strain Poisson's Ratio σ = lateral strain / longitudinal strain ''' Determination of Elasticity Modulus Elastic Energy Strain Energy = 1/2 load x extension Strain Energy per unit volume = 1/2 x (Strain)2 Strain Energy is defined as an elastic potential energy gained by a wire during elongation by stretching force . Application of Elasticity = Liquids = Molecular Theory Surface tension is a molecular phenomenon and it's origin lies in electromagnetic forces . Intermolecular Forces : 1) Cohesive Force : The force of attraction between two molecules of the same substance . 2) Adhesive Force : The force of attraction between two molecules of different substances . Range of Molecular Forces The maximum distance between two molecules up to which intermolecular forces are effective is called range of molecular attraction . Sphere of Influence An imaginary sphere drawn with given molecule as centre and radius equal to the molecular range is called the sphere of influence . Surface Energy The Potential Energy per unit area of the liquid surface under isothermal condition is called surface energy per unit area . Surface Energy = T(dA) Surface Tension The force per unit length acting at right angles to an imaginary line drawn on the free surface of liquid is called surface tension . Surface Tension (T) = F / L Also , T = Work Done / Change in Area (Multiplying displacement on Numerator ad Denominator) Or , T = Surface Energy / dA Angle of Contact When a liquid is in contact with a solid , the angle between tangent drawn to the free surface of the liquid and the surface of solid at the point of contact measured inside the liquid is called angle of contact . 1) For a given solid-liquid pair , the angle of contact is constant . 2) The value of angle of contact depends upon nature of liquid and solid in contact . 3) It depends upon medium which exists above the free surface of liquid . 4) The angle of contact changes due to impurity . 5) The angle of contact changes with temperature . 6) If θ is acute , Adhesive Force > cohesive force , liquid rises in the capillary tube and liquid meniscus is concave . 7) If θ is obtuse , cohesive force > Adhesive Force , liquid gets depressed in the tube and the liquid meniscus is convex . Capillarity The phenomenon of rise or fall of a liquid inside a capillary tube when it is dipped in a liquid is called capillarity . Surface Tension (T) = rhdg / 2cosθ Thus , we can calculate the surface tension of a liquid , by immersing a capillary tube in it , and measuring the rise or fall in liquid . h = h + r/3 Vertical Force due to S.T. F = 2πTcosθ '''Jurin's Law h α 1/r For convex meniscus in the capillary tube , the angle of contact should be obtuse . For Concave meniscus in the capillary tube , the angle of contact should be acute h1/h2 = r2/r1 Soap Bubbles 1) W = 2T - 4πR12 = 8πT- R12 2) for a liquid drop , 3) W = 4πT (r22 - r12) 4) Excess Pressure P = 4T / r 5) Pressure inside drop of a liquid P = 2T / r 6) Resultant Radius of two superpositioning bubbles is given by , r = sqrt (r12 + r12) 7) Total PRessure = hρg + 2T/r 8) P α 1 / r Effect on Surface Temperature Effect of impurities Surface Tension increases due to highly soluble impurities and decreases due to sparingly soluble impurities . Effect of temperature Surface tension of a liquid decreases with rise in temperature . T = T0 (1 - αθ)Category:Physics